There is no unique way to formulate dynamical system for \(f(R)\)  gravity theories (or any theory whatsoever). The only requirement is that we should be able to obtain an autonomous system. Over the past ten years there has been a considerable amount of work done on exploring the cosmological dynamics of \(f(R)\)  gravity. It is worth mentioning that this review has mostly focused on using variables that lead to a non-compact phase space. As shown in Sec. , one can define variables which are positive definite throughout phase space, compactifying the phase space and allowing for a detailed analysis of the asymptotics and other features such as the existence (and stability) of Einstein Static points [1]} and possible cyclic behaviour [2]}. Finally, all the methods discussed here can be easily extended to Bianchi models [3]}, [4]}. In the case of Bianchi I cosmologies, it was shown that the existence of an additional scalar degree of freedom leads to the possibility of both past and future isotropic states [5]}. In conclusion, the dynamics of \(f(R)\)  gravity is an extremely rich area of study and there remains still much interesting work to be done.
